Solving chess

Matthew, do you realize what you're doing? You're twelve years old and you're debating basic applications of computer science and mathematics with adults who have considerable experience in these fields. I'm glad to see that you've moved past that circular "computers programmed by humans say that white will win, so humans must now trust computers and accept that white will win" argument, but a rudimentary grasp of statistics won't help you either. While it is not impossible that white's first move advantage can convert into a forced win, there is nothing you can do to prove it either way. Trust me. It's better to say "I don't know" than to make erroneous arguments.

Did you try those things that I asked you to do? That is, did you compare computer analysis on the lines "1. e4 e5" and "1. e3 e5 2. e4" (or a similar line where white surrenders tempo to black)? Analysis at lower depths should be more revealing. And did you try to pit a computer against itself to see if it could convert that opening advantage each time? After all, if the computer has a winning advantage from the start, it should keep on winning, right?

Here's another fun experiment: start with a regular chess board, and determine the numerical advantage with an engine. Remove the a-pawns from both sides, then determine the advantage again. Then remove the b-pawns and do the same. Keep doing this until you are left with kings only (a dead draw). How does the advantage evolve with the removal of each piece? You can keep experimenting by starting over and removing the pieces in a different order.

Hi Matthew,

Let me try to show you the point: "Put the following diagram in your computer. If it has an endgamebook, turn it off."

Tell me what is the evaluation?

Also computers favor white at checkers because off the first move. Checkers is proven to be a draw

Uh, white seems to be a rook up?

@Schubomb, smart people think about what other people write and learn from them when they can. At the moment you are a very long way from being the most knowledgeable person here or the best at chess, but you can improve if you aim to learn. This won't happen if you always believe you are right regardless of the truth.

You need to be more careful with your arithmetic. White winning 10% and drawing 90% makes the difference between his score and black's score 10%. You can choose to include or not include the 45% of the time each draws, it gives the same answer either way. This is entirely different to the ratio between white's score and black's score which does depend on whether the draws are counted (and is where you got infinity from). To put it simply, addition is not the same as multiplication (and subtraction is not the same as division).

Ok, fair enough, the difference it is. However, I do hope you're trying to be ironic or sarcastic about the bits I bold. Otherwise, you're a pretty big hypocrite. Also, the bit I bolded in the nested quote has no basis in fact as far as I've seen.

@Schubomb, I suggest you look up the meaning of the words irony and hypocrite in the dictionary, as you have misused them.  Note that my bluntness was a response to you insisting you were right when you were not. You have made several good points as well. I am confident that all four assertions in the paragraph you have emboldened are precisely true for everyone here not just you.

(1) You are a very long way from being the most knowledgeable person here.

A very long way. Many people here have decades of experience and knowledge more than you, and some of them have are expert in fields about which you know virtually nothing. For every person here, there are others who are far more knowledgable about something, since people have to specialise.

(2) You are not the best at chess here

Check your rating. Of course this applies to all of us (except the highest rated non-cheater, whoever that might be ). That doesn't mean you can't aim to be (of course hardly any of us achieve such aims).

(3) You can improve if you aim to learn

You disagree with this? Perhaps you have already attained supreme enlightenment and perfection? [Now that's an example of irony ]

(4) This won't happen if you always believe you are right regardless of the truth

You've proved you don't do this by accepting my point at the end of the last post. Well done.

Also, I see you emboldened an earlier statement that the advantage of the first move had a stronger influence on the result of the game for stronger players. This is what I would expect, and it is proven by the statistics, because the score is higher for white in games between stronger players than it is in games between weaker players. In my 4 million game database, I have the following scores for white. Spot the trend? [It is statistically significant, whereas the very small samples in world championship matches are almost certainly not]

 Both rated 2600+     55.6%
 Both rated 2500+     55.3%
 Both rated 2400+     55.1%
 Both rated 2300+     54.9%
 Both rated 2200+     54.6%
 Both rated 2100+     54.5%
 Both rated 2000+     54.3%

Just thinking, since we are confident chess between perfect players would end in a draw, one would expect there to be a rating above which the practical advantage for white would start to decrease. However, it is quite unlikely that this rating is as low as 2800. People play differently in world championship matches to tournaments, and this could affect the statistics. It would be very interesting to look at the results between computers at different levels (>2900, >3000, >3100) and see if these exhibit any decreased advantage for white. I would not expect this to be visible until the fraction of draws gets very high (80-90%, perhaps), which is far from being the case in current top computer games.

Yes, computer are not reliable. But this has nothing to do white's extra tempo being enough to win. I'm talking the 1/3 pawn.

"56% 1/2-1/2  enough said"

Lol, you can't win that easy! A few reasons, 1. this is a very small number of games your dealing with. 2. did you read my post about the micro errors causing those draws?

"when you're lower rated even than me"

You have no idea how hard my rating swings, this is about as low as it gets.

Elroch, it doesn't make sense for you to be this patronising. You have no idea what my level of expertise is at anything except for the small knowledge of my chess skill which my online rating affords you. Not only that, but I've never even claimed to be the most knowledgable here, chess-wise or otherwise, nor implied it, so I don't even know why you bring it up.

I do find it pretty sad, however, that you assume that I can't be the most generally knowledgable person here (for all either of us know, I may well be), presumably based entirely on my (not even that young) age. Surely with age like yours comes experience, and with experience comes the knowledge that judging someone's level of skill and knowledge based upon their age (and chess rating) is complete folly, right?

And of course some people specialise in things I know nothing about, just as I specialise in some things almost certainly no-one else on this thread knows anything about. Specialisation does not make knowledgability, nor do decades of experience (though that does help - but only help, not guarantee).

Don't think here that I'm assuming my own superior knowledgability to anyone else here (which seems likely for you to do, based on your posts addressed to me so far). I'm just dismayed that you would assume the opposite without justification (unless you're being ironic).

I have not misused irony nor hypocricy. It would be ironic were you to impugn my knowledgability without actually knowing how knowledgable I am, at best (look up ironic humour sometime), since (ironically) it shows foolishness on your part (I'm being generous and assuming you were making a weak joke). At worst, it would be hypocritical.

Note that I have not insisted that I am right, except in a rhetorical sense, intended to show Matthew11 the folly of his own insistence that he is right, and challenging him to find a counterexample of my claims. Just because you fail to understand the (not particularly subtle) nuances of what I write, doesn't make it a failing of mine.

"You can improve if you aim to learn" - No, mr internet stranger, being older than me does not entitle you to such banal patronisation of me. How about you improve your social skills and humility, since those are quite clearly lacking?

Now, as regards the more interesting part of your post:

Do the samples from your database have some kind of statistical correlation with how closely rated the players are, or is it purely as it appears, just any two players with ratings above the number given? Because you know that that is a completely useless statistic unless it's controlled for at least relatively even skill. Disregarding that, the trend shown, even if it has any meaning, might mean that the players involved in higher ratings are more conversant with opening theory which helps white consolidate the opening advantage or keep it for longer, rather than let it whittle away like it often tends to, rather than any actual technical skill difference in their unplanned moves. It would make intuitive sense that the higher the rating, the more resources and time they can justify into opening databases and study and prep.

That's not to say that this opening prep advantage doesn't have its own meaning. But all it may mean is that with greater skill and/or prep, the harder it is and the longer it takes for white's seeming opening advantage to get whittled away.

And this is about as low as mine gets. What's your point? You want to make a point of how inconsistent you are? Look, it's cool, you're 12 and probably pretty good for 12. I'm just saying that you have your flaws like everyone else.

Now instead of trying to toot your own horn, how about you don't take my quote out of context and realise that it doesn't matter how hard your rating swings, you aren't as good in chess understanding as the myriad grandmasters I referenced in context who say that chess is a draw or the computers which draw against each other, so you claiming that any advantage is equal to a win is just pathetically invalid, frankly.

The explanation is probably rather different. It's more about what the players are trying to achieve in a game. A top player is able to choose opening lines and plans in a way which either tries to ensure the draw or to give the best chance of winning. Since world championships are about achieving slightly more wins than the opponent rather than the maximum score, the majority of the time both players are aiming for a draw with black and aiming for a win with white (as is often mentioned in commentary). This is not the case as often in tournament play, where it may be worth taking the risk of going for a win with black to aim for a big prize. As a result, black wins in world championship matches are far less common, because it is unusual for a player who is trying to ensure a draw from the outset (with a move disadvantage) can achieve a win. Well, that's my view, anyhow.

 1. Since we agree computers are not reliable, then why do you think the extra tempo that white has is worth 1/3 off a pawn. Please give me your source.

2. Also the diagram I posted proofs that having 2 extra knights, a centralised king and a tempo is not always enough to secure a win.  (so not every tiny advantage can always convert into a win)

You claim that white has enough to win from the startingposition with one tempo. This sounds as you probably know yourself ridiculous. You try to back this up by statistics from imperfect games. Which mean nothing at all if you are debating the perfect game.

You have gotten a debate going, which I think was your true purpose.

Your responses to some posts suggests to me that you are playing and trying to win a discussion. Which perhaps in your not yet totally develloped mind is working. In fact it is not.

If you want to be educated: start listening. dont be thick. 

If you want to play: go to the forum "fun with chess" many people will play with you there. If you want I'll even join your thread there and disprove 'melons are blue on the inside before you cut them open, proof me wrong'-statement.  ok?

@Schubomb, you make the interesting point that in my breakdown of the games at different levels, the higher bands were increasingly narrow. I wouldn't expect this to skew the results because the stronger player will have white just as often as black, but it is plausible that there could be some sort of second order effect.

Using 100 point rating bands instead, white's winning percentages are as follows. Note that the trend extends all the way up to 2800 (when tournament games as well as match games are included).

2000-2099   53.2%
2100-2199   53.7%
2200-2299   53.9%
2300-2399   54.4%
2400-2499   54.6%
2500-2599   54.9%
2600-2699   55.3%
2700-2799   55.6%

No, we aren't talking about statistics, we're talking about the perfect game, because only that determines the value of the position. Statistics do not change the perfect game. Black loses more often because no matter how good any human on earth is, they still might allow white's advantage to transfer into a larger advantage (because they don't play perfectly).

It seems to comes down to opinion. If white's advantage can turn inot a win can't be proven ether way, at least, not until chess is solved. I'm not the only one who thinks chess is a win for white, sorces: "Unbeatalble Openings" White to play and win"  And things like that. What I'd like to know is why black is said to have more chances to mess up.

Wating for SchuBomb's sarcastic "I'm better than you" comment. =)

I call trolling. There is no way anybody is this stupid and still articulate.

Oh no, I'm quite glad that you at least think it comes down to opinion, rather than your previous "white has a .15 advantage and there's NO WAY to take that away, therefore white must have a win" talk. At least you're open to new ideas now :)

There are indeed people who think white wins, including former world correspondence chess champion Hans Berliner, who considered d4 a win. However, even he said "It is possible that the rules of chess are such that only some number of plausible-appearing defences to 1.d4 can be refuted.". I haven't read his book that details the claim, but at least he also seems open to the idea that there can be a genuine defense for black. I don't know either of the books you mention either (it's pretty impossible to search for without you telling us the author) but I'd imagine they're less well informed and lesser in chess understanding than Berliner.

My own view corresponds with that of GM Larry Kaufmann: "I don't believe that White has a forced win in Chess. I do however believe that with either 1.e4 or 1.d4, White should be able to obtain some sort of advantage that persists into the endgame. If chess were scored like boxing, with drawn games awarded by some point system to the player (if any) who came 'closer' to winning, then I believe White would indeed have a forced win in theory."

(with my own addition that I think 1. Nf3 is just as good, if not better than, either e4 or d4 - at best I think it is a superior move because it is flexible, at worst I think it would transpose into a suitably advantageous e4 or d4 opening with best play)

I still find it hilarious that it can't be proven yet that white isn't in fatal zugzwang and loses by force. It would require every single one of the first 20 moves to be so much worse than doing nothing to the point of making it losing by force, and I don't think that's so, but it can't be proven wrong, yet...

Now we're getting somewhere, and while I consider 100 points to be too wide still, I imagine with narrower bands the trend would stay the same. I would be interested in seeing, with narrower bands, whether the trend, while still increasing, plateaus somewhat (but there may not be a sufficient sample size to do this, or  to get smooth transitions. We see, in .1% multiples, 5, 2, 5, 2, 3, 4, 3 changes for each hundred, which shows no sign of speeding up or slowing down really, but who knows.

My tentative opinion on this is that the lower the level and the faster the time controls, the faster the opening advantage dissipates, and typically, especially at club level, it will end as win or loss with relatively few draws. The higher the level, the longer the opening advantage persists and the slightly better white scores, but despite this, there are more draws (as skill approaches perfection, the result tends more and more towards the result of the perfect game).

It is similar to how checkers, when Marion Tinsley was playing chinook, was practically at perfection already, and over 80% of their games ended in draws. Guess what happened a decade later? Checkers was proven to be a draw with best play, despite the first player's opening advantage. (That's for you, Matthew11)

I have no doubt that the 100 point bands are more than adequate to exhibit the strong correlation. An alternative is to use very narrow bands for one player, and not to restrict the rating of the opponent, making the results rather more relevant to the games of an individual player. Feel free to do any other analysis you like.

The graph shows no sign of plateauing up to the highest ratings achieved by humans. Interestingly, computer versus computer games exhibit quite similar advantage for white, with results of the strongest computers showing 56.4% for white. (Note that this is slightly higher than in the human games, and the strongest computers are significantly stronger than the strongest humans. It is questionable to add computer games to the same graph, but would be interesting to examine a similar graph for computers.

Doubling computer speed increases Elo rating by about 60 points and increases search depth by about about 0.4 ply (very roughly). There is no evidence to suggest this trend disappears even when depths of 40 ply or more are being used, but there is evidence that the rate of increase of strength diminishes [Also this]. It is reasonable to assume that increases in strength will continue to be achievable until the number of nodes not in an endgame tablebase starts to decrease. This might be expected to be the case when perhaps 60 moves have been played and 200 ply of search depth is available (again, very rough figures).

The consequence of these considerations is that (barring physical constraints) computer chess might improve up to about 200 ply of search depth, which could give a rating of over 10000 (roughly). If the trend exhibited in the graph in post #146 continued (this is a hypothesis, not a prediction), a computer with a rating of 10000 would score over 80% with white against other computers of similar rating. This would mean white was increasingly able to deny black the draw with near perfect play, rather than black increasingly deny white the win.

Of course such an extrapolation is speculative, but no more so than inferring from the results of human players with ratings <2900 that chess is probably a draw (because draws are increasingly common as ratings rise towards 2800). The difference between a postulated Elo 10000 computer and current experience is far greater than the difference between Kasparov and a beginner with a rating of less than 1000, and who would rely on the intuition of such a beginner? A similar argument applies to any discussions based on the evaluations of current computers with feeble () 40-ply search depth.

In conclusion, I find it entirely plausible that chess is a win for white, because the best evidence available shows white's advantage is increasing with strength, and we have no evidence yet that this increase will stop. On the other hand it is plausible that chess is a draw, but I would say the evidence for this is similarly inconclusive, based as it is on games that are undoubtedly extremely weak compared to hypothetical perfect chess.